JEE Main 2024 Mathematics question
Let the set S = {2, 4, 8, 16, ....., 512} be partitioned into 3 sets A, B, C with equal number of elements such that A ∪ B ∪ C = S and A ∩ B = B ∩ C = A ∩ C = φ. The maximum number of such possible partitions of S is equal to:
Answer: (A)
Solution
S has 9 elements, so the number of ways to split them into three unlabelled-by-size groups of 3 assigned to A, B, C is 9!/(3!)³ = 1680.